Khalfallah, M. Faiez (2023) Assimilation de données pour les équations aux dérivées partielles PRE - Research Project, ENSTA.
This report examines the efficiency of the finite element method in the context of data assimilation with a method based on a space-time variational formulation, the so-called 4d-var methods. Using a preliminary simulation based on the Laplacian equation, we evaluate the performance of this method on a simple mathematical problem. Next, we focus our analysis on the heat equation, aiming to determine how the finite element method performs in more complex scenarios compared to non-conforming methods. Through detailed experiments, we evaluate the performance of the finite element method in terms of accuracy and cost. This study offers an in-depth perspective on the advantages and limitations of the finite element method for solving data assimilation problems, and contributes to a better understanding of its potential in various scientific and engineering fields.
|Item Type:||Thesis (PRE - Research Project)|
|Uncontrolled Keywords:||Data assimilation, Partial differential equations, Finite elements, Numerical methods|
|Subjects:||Mathematics and Applications|
|Deposited By:||Faiez KHALFALLAH|
|Deposited On:||28 août 2023 16:43|
|Dernière modification:||28 août 2023 16:43|
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